Mathematica Revisited

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Mathematica Revisited

• Redesigning a Math Education Museum Exhibit
• Nancy Daniels, Karen Jia, Nina Weber, Jim Vanides
• Stanford University Learning Design and
  Technology
• November 2001

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(No Transcript)
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Overview

• Proposal
• Museum Observations
• Learning Theory
• Exhibit Redesign and Extensions
• User Feedback
• Next Steps
• Personal Reflections

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Proposal

• (describe initial proposal)
• Modified Redesign one of the Mathematica
  exhibits to improve its appeal and learning
  impact

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The Multiplication Cube
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Museum Observations

• pictures
• field notes redesign brainstorm

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Museum Observations
(Nancy describe an observation, add a
picturemake duplicate slides as you see fit)
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Museum Observations
Only one child was observed reading the
surrounding notes
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Learning Theory How do we get them to know?
Vbhl Is that all?
From the Mathematica exhibit
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A Cybernetic Solution

• Learning should be
• interactive.
• multi-sensory.
• accessible.

• built on prior experience.
• conveyed through multiple representations.
• beyond just knowing a formula.

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The Challenge

• Language of math can be confusing.
• 2 35 but 1/2 1/3 5/6
• So much of math, relies on a solid foundation.
  If you miss one part, you may not get the next
  point.
• There are many constraints in the classroom
  (materials, time, of students, teaching
  philosophies of parents of teachers)
• Assessment results are only estimates of what a
  person knows and can do.

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My experience in the classroom
Learning entails the transformation of naïve
understanding into more complete and accurate
comprehension Knowing What Students Know, p4.

• Some students just dont get what were teaching
• Some students really get the essence of what
  were teaching
• Some students get a little bit of what were
  teaching

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How can we tell a student knows?

• A variety of assessments
• Observations
• Confusion

• Boredom
• Extending the activities
• Misbehavior

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Inspiration Research and Theories

• Not all children learn in the same way and
  follow the same paths to competence.
• --Knowing What Students Know, p. 4.
• Our knowledge cant be a representation of that
  real world, but only as a key that unlocks
  possible paths for us.
• --Ernst von Glaserfeld, p.194.
• Constructivist theories assume that knowledge is
  actively constructed and reconstructed by the
  learner out of his or her experiences in the
  world.
• --Minds in Play, p.10.

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Learning Theory Highlights

• Ground the groundless. Make connections.
• Build on what students know. Learning is
  recursive.
• Vary the interactions by creating a multi-sensory
  experience touch, hear, and see.
• Think clearly about the goals before getting
  started. What do you want them to know?

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References

• Knowing What Students Know The Science and
  Design of Educational Assessment, Washington,
  DC National Academy Press,2001.
• Kafai, Yasmin, Minds in Play Computer Game
  Design as a Context for Childrens Learning, New
  Jersey Lawrence Erlbaum Associates, Publishers,
  1995.
• Von Glaserfeld, Ernst, The Construction of
  Knowledge Contributions to Conceptural
  Semantics.
• Seeing Fractions
• www.exploratorium.edu

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Exhibit Redesign The Multiplication Cube

• Exhibit Layout
• Control Panel UI
• Museum and Classroom Extensions

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New Exhibit Layout (Nancy)

• (insert slides and pictures)
• (include what were recommending and why)

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New Control Panel UI - objectives

• Provide the users with a clearer connection
  between the physical model and the math by adding
  an algebraic representation
• Improve the users conceptual understanding of
  multiplication by changing the lighting sequence
  to match the algebraic operation
• Clarify how the control panel is linked to the
  physical light array converting the user
  interface into a flat panel touch-screen display
  that includes a representation of the model

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Current Control Panel
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

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START
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

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START
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

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START
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

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START
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

8
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Watch!
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

8
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Watch!
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

8
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Watch!
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

8
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Watch!
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

8
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Watch!
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

8
8
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5
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Watch!
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

8
8
7
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Watch!
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

8
8
7
7
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5
5
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Watch!
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

8
8
7
7
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5
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x
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Watch!
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

8
8
7
7
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5
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Watch!
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

8
8
7
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

8
8
7
7
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Watch!
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• Multiplication Machine
• It will multiply the numbers you choose from
  these three dimensions of numbers.
• press only one button in each direction
• press the start button to multiply

8
8
7
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Watch!
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Museum and Classroom Extensions

• Cube City (classroom)
• Multiplication Activities (touchscreen)
• Multiplayer Multi-Cube
• Online Fraction Game

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Cube City (Nancy)
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Multiplication Kiosks/Stations (Karen)
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Multiplayer Multiplication Cube - Objectives

• Increase Mathematical Discourse and collaboration
  at the exhibit
• Increase the cognitive challenge by providing an
  alternative game that works backwards from a
  target number
• Encourage mathematical inquiry

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Multiplication Machine Player 1
It will multiply the numbers you and your
team-mates choose from these three dimensions of
numbers. Choose which game you would like to
play Free Explore or Find-a-Number Press
one button from your dimension, while your
team-mates pick their own numbers from their
dimensions.
1
2
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Free Explore
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Find-a-Number
x
x

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Multiplication Machine Player 1
Work with your team to find three numbers, that
when multiplied together, equal the Challenge
Number below
1
2
Make This Total
3
60
4
5
6
7
8
Find-a-Total
x
x

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Multiplication Machine Player 1
Work with your team to find three numbers, that
when multiplied together, equal the Challenge
Number below
1
2
Make This Total
3
60
4
5
6
7
8
Find-a-Total
4
4
1
1

x
x
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Multiplication Machine Player 2
8
7
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5
4
Work with your team to find three numbers, that
when multiplied together, equal the Challenge
Number below
3
2
1
Make This Total
60
Find-a-Total
4
4
1
1

x
x
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Multiplication Machine Player 2
8
7
6
5
4
Work with your team to find three numbers, that
when multiplied together, equal the Challenge
Number below
3
2
1
Make This Total
60
Find-a-Total
4
12
3
1

x
x
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Multiplication Machine Player 3
8
7
6
5
Work with your team to find three numbers, that
when multiplied together, equal the Challenge
Number below
4
3
2
1
Make This Total
60
Find-a-Total
4
12
3
1

x
x
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Multiplication Machine Player 3
8
7
6
5
Work with your team to find three numbers, that
when multiplied together, equal the Challenge
Number below
4
3
2
1
Congratulations !
60
Play Again!
4
60
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x
x
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Online Fraction Game - Objectives

• Help users see that fractions are related to
  multiplication
• Build a stronger conceptual understanding of the
  meaning of a fraction through multiple
  representations (grid, numeric, bar)
• Model the simplification of fractions

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Fraction Fun!
There are two ways to play. Choose one of the
buttons below
press buttons to build a fraction
choose numbers to build a fraction
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Fraction Fun!
There are two ways to play. Choose one of the
buttons below
press buttons to build a fraction
choose numbers to build a fraction
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Fraction Fun!
Move the hand up or down to select the numerator
0
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Start Over
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Fraction Fun!
Move the hand up or down to select the numerator
1
64
Start Over
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Fraction Fun!
Move the hand up or down to select the numerator
12
3

64
16
Start Over
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Fraction Fun!
Move the hand up or down to select the numerator
12
3

64
16
Start Over
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Fraction Fun!
There are two ways to play. Choose one of the
buttons below
press buttons to build a fraction
choose numbers to build a fraction
64
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Fraction Fun!
There are two ways to play. Choose one of the
buttons below
press buttons to build a fraction
choose numbers to build a fraction
64
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Fraction Fun!
Press as many buttons as you would like, and see
how the pattern represents a fraction
0
of lights on
out of a total of
64
Start Over
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Fraction Fun!
Press as many buttons as you would like, and see
how the pattern represents a fraction
1
of lights on
out of a total of
64
Start Over
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Fraction Fun!
Press as many buttons as you would like, and see
how the pattern represents a fraction
2
of lights on
1

out of a total of
64
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Start Over
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Fraction Fun!
Press as many buttons as you would like, and see
how the pattern represents a fraction
3
of lights on
out of a total of
64
Start Over
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Fraction Fun!
Press as many buttons as you would like, and see
how the pattern represents a fraction
4
of lights on
1

out of a total of
64
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Start Over
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User Feedback

• comments from users
• What we did with it

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Next Steps

• Incorporate Additional User Feedback (Students
  Teachers)
• Debrief With Exploratorium

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Personal Reflections

• Karen .
• Nancy
• Jim Teamwork is great when it works like this
  we were all synchronized, speaking the same
  language of learning design
• Nina ..